2. SECULAR EVOLUTION OF BARRED GALAXIES

We see only snapshots of galaxy evolution, so it is difficult to study
slow processes. 1 Why do we
think that secular evolution is happening? We begin with an existence
proof - a review of how n-body
simulations account for the morphological features seen in barred
galaxies. Our suggestion that pseudobulges are constructed out of
rearranged disk gas is embedded in this larger picture of SB secular
evolution.

Barred
spiral galaxies are divided into subclasses SB(s), in which the spiral
arms begin at the ends of the bar, and SB(r), in which a complete inner
ring of stars connects the ends of the bar. In the latter case, the
spiral arms start somewhere on the ring, "often downstream from the
ends of the bar"
(Sandage & Bedke
1994).
SB(r) and SB(s) galaxies are contrasted in
Figure 6; additional SB(r) galaxies are shown in
Figure 3 and Figure 5, and
additional SB(s) galaxies are shown in Figure 7.

Some barred and oval galaxies have outer rings (R) that are 2.2
± 0.1 times
the diameter of the bar or inner disk. Outer rings in barred and
unbarred galaxies are similar
[Figure 2 and Figure 5].
Inner and outer rings are different; there is no size overlap. Some
galaxies contain both (Figure 5).

At intermediate Hubble types, when the bar is made mostly of old
stars and
the disk contains many young stars, the stellar population of inner and
outer rings is like that of the disk, not like that of the bar
(Figures 2 and 3). Inner
and outer rings generally contain gas.

In SB(s) galaxies, an almost-straight dust lane parallels the ridge line
of the bar but is displaced slightly forward in the direction of
galactic rotation. Such dust lanes are analogous to and connect up with
the prominent dust lanes seen on the trailing side of the arms in
global-pattern spirals. Examples are shown in
Figure 6 and in
Figures 7 and 8.
These dust lanes are almost never present in SB(r) galaxies
(Sandage 1961).
NGC 1512 in Figure 3 is a
rare exception.

Many barred and oval galaxies have very active star formation near their
centers, in what is conventionally identified as the bulge. Often the
star formation is concentrated in a ring.
Figures 3, 7,
and 8 show examples.

Many barred galaxies have pseudobulges that are elongated into a
structure resembling a bar. Examples are shown in
Figure 14.

Many early-type SB galaxies contain a lens in the disk - a shelf of
slowly decreasing surface brightness with a sharp outer edge. Lenses have
intrinsic axial ratios of ~ 0.85; the bar usually fills the longest
dimension. These properties are discussed in Kormendy
(1979a,
b,
1981,
1982a)
and in
Athanassoula et
al. (1982).
Lenses are sometimes seen in unbarred galaxies; NGC 1553 is the best example
(Freeman 1975,
Kormendy 1984).
Lenses in early-type galaxies look similar to oval disks in late-type
galaxies (Section 3.2); it is not clear
whether or not they are physically similar. Lenses are illustrated in
Figures 2 and 5.

Figure 3.NGC 1512, an SB(r)ab galaxy imaged with HST by
Maoz et al. (2001).
This figure (courtesy NASA and ESA) illustrates the stellar population
of inner rings. As is common in intermediate-Hubble-type galaxies, the
bar in NGC 1512 is made of old, red stars and the disk is
made of young, blue stars. This figure shows that the inner ring has
the same stellar population as the disk, not the bar. Also seen at
center is a nuclear star-formation ring that is shown at higher
magnification in Figure 8 and the
start of a well-developed, curved dust lane (cf.
Figures 6-8)
that extends out of the field of view to the right. The corresponding
dust lane on the other side is visible near the central ring but not at
larger radii. The outer parts of NGC 1512 are illustrated by
Sandage & Bedke
(1994),
who note that NGC 1512 is morphologically normal except for some
distortion of its outer spiral structure (not shown here) by a tidal
encounter with neighboring NGC 1510.

These
features can be understood at least qualitatively as results of secular
evolution driven by nonaxisymmetric gravitational potentials. An exact
correspondence between n-body simulations and observations
cannot be expected, because real galaxies have a complicated interplay
between gas, star formation, and energy feedback from massive young
stars back into the interstellar medium. Such effects, along with the
self-gravity of the gas, are often omitted from simulations and at best
are included only approximately. Nevertheless, n-body simulations
have been conspicuously successful in reproducing the structure of
barred galaxies.

To understand bar-driven evolution, we need to dip briefly into the
dynamics of bars. An in-depth review is provided by
Sellwood &
Wilkinson (1993).
Here we need a primer on the nature and importance of orbital resonances.

Seen from an inertial frame, an orbit in a galactic disk is an unclosed
rosette. That is, there are a nonintegral number of radial oscillations
for every revolution around the center. However, in a frame of
reference that rotates at the average angular velocity of the star, the
star's mean position is fixed, and its radial oscillation makes it move
in a small ellipse around that mean position.
2
Any global density pattern such as a bar that rotates at the above
angular velocity will pull gravitationally on the star in essentially
the same way at all times and will therefore make large perturbations
in its orbit. Corotation is the strongest of a series of resonances in
which the pattern repeatedly sees the star in the same way.

For
example, there is another rotating frame in which the star executes two
radial oscillations for each circuit around the center. If a bar
rotates at this angular velocity, it sees the stellar orbit as closed,
roughly elliptical, and centered on the galactic center
(Figure 4). This is called inner Lindblad
resonance (ILR). It occurs when the pattern speed of the bar is
p
= -
/2, where
is the average
angular velocity of revolution of the
star and is its
frequency of radial oscillation. The limit of small
radial oscillations is called the epicyclic approximation; then
2 =
(2V / r)(V / r + dV / dr),
where V(r) is the circular-orbit rotation curve
(Mihalas & Routly
1968
provide a particularly transparent discussion).

Figure 4. (Top) Frequencies
(r) =
V(r) / r and
±
/2, where
2 =
(2V / r) (V / r + dV / dr) is
the epicyclic frequency of radial oscillations for almost circular
orbits. This figure
(Sparke &
Gallagher 2000)
is for a Plummer potential, but the behavior is generic. For a pattern
speed p,
the most important resonances occur where
p =
(corotation),
p =
+
/2 [outer Lindblad
resonance (OLR)], and
p =
-
/2 [two inner Lindblad
resonances (ILR), marked with vertical dashes]. (Bottom) From
Englmaier &
Gerhard (1997),
examples of the principal orbit families for a bar oriented at 45°
as in Figure 7.
The elongated orbits parallel to the bar are the x1
family out of which the bar is construc ted. Interior to ILR (or outer
ILR, if there are two LRs), the x2
family is perpendicular to the bar. Near corotation is the 4:1
ultraharmonic resonance; the almost-square orbit makes four radial
oscillations during each circuit around the center. Since the principal
orbits change orientation by 90° at each resonance shown, they
must cross near the resonances.

Outer
Lindblad resonance (OLR) is like inner Lindblad resonance, except that
the star drifts backward with respect to the rotating frame while it
executes two radial oscillations for each revolution:
p =
+
/2.

Resonances are important for several reasons.
Figure 4
shows generic frequency curves and the most important periodic orbit
families in a barred galaxy. We can begin to understand how a
self-consistent bar is constructed by exploiting the fact that
-
/2
varies only slowly with radius (except near the center, if there is an
ILR). Calculations of orbits in a barred potential show that the main
family of orbits (called x1) is elongated parallel to
the bar between ILR and corotation. Bars are largely made of
x1 orbits and similar, nonperiodic orbits that are
trapped around them by the bar's self-gravity. Typical
x1 orbits are shown in the bottom panel of
Figure 4.
They are not nearly circular, but the essence of their behavior is
captured if we retain the language of the epicyclic approximation and
say that orbits of different radii look closed in frames that rotate at
different angular velocities
-
/2. But if
-
/2 varies only a
little with radius, then it is possible to pick a single pattern speed
p
in which the orbits precess almost together. If they precessed exactly
together, then one could make a bar by aligning elongated orbits as in
the bottom panel of the figure. Because
-
/2 is not quite constant,
it is the job of self-gravity to make the orbits precess not
approximately but exactly together. This idea was used to understand
self-consistent bars by
Lynden-Bell &
Kalnajs (1972)
and by Lynden-Bell
(1979)
and to demystify spiral structure by
Kalnajs (1973)
and by
Toomre (1977b).
They were following in the pioneering footsteps of
Bertil Lindblad (1958;
see section 20 of
Lindbald 1959).

Calculations of orbits in barred potentials reveal other orbit families
(e.g.,
Contopolous &
Mertzanides 1977;
Athanassoula 1992a,
b;
Sellwood &
Wilkinson 1993),
only a few of which are relevant here. Next in importance is the
x2 family, which lives interior to ILR and which is
oriented perpendicular to the bar
(Figure 4,
bottom). Between corotation and OLR, the principal orbits are elongated
perpendicular to the bar, and outside OLR, they are again oriented
parallel to the bar. Near corotation is the 4:1 ultraharmonic resonance
in which a star executes 4 radial oscillations for every revolution:
p =
-
/4. We need these
results in the following sections.

The important consequence is emphasized by
Sellwood &
Wilkinson (1993):
"Not only do the eccentricities of the orbits increase as exact
resonance is approached, but the major axes switch orientation across
all three principal resonances, making the crossing of orbits from
opposite sides of a resonance inevitable" (bottom panel of
Figure 4).
This is important mainly when the orbits are very noncircular, as they
are in strongly barred galaxies. Now, orbits that cross are no problem
for stars. But gas clouds that move on such orbits must collide near
resonances. Dissipation is inevitable; the consequence is an increase
in the gas density and star formation. This heuristic discussion helps
to explain the numerical results reviewed in the following sections, in
which gas tends to build up in rings and to form stars there.

The essence of the response of gas to a bar is captured in figure 3 of
Simkin, Su &
Schwarz (1980),
reproduced here as Figure 5.
Outside corotation, gas is driven outward by the angular momentum
transfer from bar to disk that makes the bar grow. This gas collects
into an outer ring near OLR. As discussed earlier, outer rings are
oriented perpendicular to the bar when they are interior to OLR; this
is the usual situation
(Kormendy 1979b,
Buta 1995).
At radii well inside corotation, gas falls toward the center. This is
the gas that is believed to make pseudobulges. Within an annular region
around corotation, gas is collected into an inner ring near corotation
or near the 4:1 ultraharmonic resonance.

The reason why SB(r) and SB(s) galaxies are different was investigated by
Sanders & Tubbs
(1980).
They simulated the response of gas to an imposed, rigid bar potential
that they grew inside a disk galaxy. Examples of the steady-state gas
response are shown in Figure 6.
In the top two rows of panels, the strength of the bar increases from
left to right, either because the ratio of bar mass to disk mass
increases (top row), or because the bar gets more elongated (second
row). In both cases, weak bars tend to produce an SB(s) response, while
strong bars produce ring-like structures that resemble SB(r) galaxies.
If the bar gets too strong (top-right panel), the result does not look
like a real galaxy. The bottom row of simulations explores the effect
of varying the bar's pattern speed. Rapid pattern speeds produce
dramatically SB(s) structure. Slower pattern speeds in which corotation
is near the end of the bar produce inner rings. Very slow pattern
rotation (right panel, in which corotation is at 3 bar radii) produce
responses that do not look like real galaxies. This is because
p
is now so small that the radius of ILR is large. Inside ILR, closed gas
orbits align perpendicular to the bar. These can never have
substantially the same radius as the bar, as they do in the
bottom-right simulation in Figure 6.
If the response to the bar were perpendicular to the bar over most of
the radius of the bar, it would be impossible to make that response add
up to a self-consistent bar. Pattern speeds are never so slow that
corotation radii are so far out in the disk that the entire bar is
inside ILR. This was possible in
Sanders & Tubbs
(1980)
only because the bar was inserted by hand and given a chosen (not a
self-consistent) pattern speed. Theoretical arguments tell us that bars
end inside or near corotation
(Contopoulos 1980,
Sellwood &
Wilkinson 1993).
Observations agree
(Kent 1987b;
Merrifield &
Kuijken 1995;
Gerssen, Kuijken &
Merrifield 1999,
2003;
Debattista &
Williams 2001;
Debattista, Corsini
& Aguerri 2002;
Aguerri, Debattista
& Corsini 2003;
Corsini, Debattista
& Aguerri 2003;
see
Elmegreen 1996
for a review) except in late-type galaxies in which Vr rotation curves imply that the bar is safely clear of ILR anyway
(Elmegreen 1996;
Elmegreen, Wilcots
& Pisano 1998).

Figure 6. Contours of steady-state gas
density in response to a bar (adapted from
Sanders & Tubbs
1980,
who also show intermediate cases). The bar is horizontal and has a
length equal to four axis tick marks. The top row explores the effect
of varying the ratio MB / MD of bar
mass to disk mass. The second row varies the bar's axial ratio b
/ a. The third row varies the bar pattern speed, parameterized
by the ratio rcor / a
of the corotation radius to the disk scale length. The middle column is
the same standard model in each row; it approximates an SB(r) galaxy
such as NGC 2523 (bottom center). The left panels
resemble SB(s)
galaxies such as NGC 1300 (bottom left). The right panels carry
the parameter sequences to unrealistic extremes; they do not resemble
real galaxies.

Figure 7. Comparison of the gas response to
a bar (model 001 by
Athanassoula 1992b)
with NGC 5236 (left) and NGC 1365 (right).
The galaxy images were taken with the VLT and are reproduced courtesy
of ESO. In the models, the bar potential is oriented at 45° to the
horizontal, parallel to the bar in NGC 5236. The bar axial ratio is
0.4, and its length is approximately half of the box diagonal. The
top-right panel shows the velocity field; arrow lengths are
proportional to flow velocities. Discontinuities in gas velocity
indicate the presence of shocks; these are where the gas density is
high in the density map at top left. High gas densities are identified
with dust lanes in the galaxies. The model correctly reproduces the
observations that (a) dust lanes are offset in the forward
(rotation) direction from the ridge line of the bar; (b) they
are offset by larger amounts nearer the center; and (c)
very near the center, they curve and become nearly azimuthal. As
emphasized by the velocity field, the shocks in the model and the dust
lanes in the galaxy are signs that the gas loses energy. Therefore it
must fall toward the center. In fact, both galaxies have high gas
densities and active star formation in their bright centers (e.g.,
Crosthwaite et
al. 2002;
Curran et al. 2001a,
b).

In an important paper,
Athanassoula (1992b)
explored the response of inviscid gas to a bar using a high-resolution
code. Her main focus was gas shocks and their relation to dust lanes.
Typical results are shown in
Figure 7.
If the mass distribution is centrally concentrated enough to result in
an ILR, then the dust lanes are offset in the forward (rotation)
direction from the ridge line of the bar. Because of the presence of
the x2 orbits - the ones that align perpendicular to
the bar inside ILR - the offset is largest near the center
(Figure 7).
The models reproduce the observation that the dust lanes in many bars
curve around the center of the galaxy at small radii and become nearly
azimuthal. Athanassoula found that the dust lanes are more curved into
an open S shape when the bar is weak; this is confirmed observationally by
Knapen,
Pérez-Ramírez, & Laine (2002)
and is illustrated for NGC 6782 in Figure 8. As
Athanassoula notes, "the resemblance between [the models and the
observations] is striking."

The important consequence of this work is that shocks inevitably imply that
gas flows toward the center. Because the shocks are nearly radial, gas
impacts them at a steep angle. Therefore much of the velocity that is
lost in the shock is azimuthal. This robs the gas of energy and forces
it to fall toward the center.

Athanassoula estimated that azimuthally averaged gas sinking rates are
typically 1 km s-1 and in extreme cases up to ~ 6 km
s-1. Viscosity is not an issue in her models, so these
estimates are more realistic than earlier ones. Because 1 km
s-1 = 1 kpc (109 yr)-1,
the implication is that most gas in the inner part of the disk - depleted
by star formation but augmented by mass loss during stellar
evolution - finds its way to the vicinity of the center over the course
of several billion years, if the bar lives that long.

In recent
years, simulations have continued to concentrate on these inner regions
of barred galaxies where dust lanes and star formation are most
important
(Friedli & Benz
1993,
1995;
Piner, Stone &
Teuben 1995;
Englmaier &
Gerhard 1997;
Salo et al. 1999;
Weiner, Sellwood &
Williams 2001a;
Regan & Teuben
2003).
The conclusions are as follows: (a) Gas flows toward the
center. (b) Star formation fed by the inflow is often
concentrated in a narrow nuclear ring. (c)
The inflow is a result of gravitational torques produced by the bar,
but its immediate cause is the shocks. In essence, these are produced
because gas accelerates as it approaches and decelerates as it leaves
the potential minimum of the bar. So it tends to pile up near the ridge
line of the bar. Incoming gas overshoots a little before it plows into
the departing gas, so the shocks are nearly radial but offset from the
ridge line of the bar in the forward (rotation) direction. The above
simulations confirm Athanassoula's conclusion that offsets happen when
the central mass concentration is large enough to allow a "sufficient"
range of x2 orbits. The agreement in morphology
between the simulated shocks and the observed dust lanes has continued
to improve. But there is an even better reason to think that they are
connected. Compelling support is provided by the observation of large
velocity jumps across the dust lanes
(Pence & Blackman
1984;
Lindblad, Lindblad
& Athanassoula 1996;
Regan, Sheth &
Vogel 1999;
Weiner et al. 2001b;
and especially
Regan, Vogel &
Teuben 1997).

What happens to the infalling gas? Star formation is almost
inevitable. The simulations, expectations from the
Schmidt (1959)
law, observations of young stars in SB nuclei, and star-formation
indicators (Section 5) all point to
enhanced star formation, often in
substantial starbursts near the center. Examples are shown in
Figure 8. NGC 4314 is a barred galaxy whose
central star formation is also illustrated in the Hubble Atlas
(Sandage 1961).
NGC 1512 is an SB(rs) galaxy whose outer parts are
shown in Figure 2. The dust lane in the bar is
best seen in the Carnegie Atlas of Galaxies
(Sandage & Bedke
1994).
NGC 6782 contains an oval disk with an embedded
bar. Finally,
NGC 4736
is a prototypical unbarred oval galaxy. It is included to illustrate
the theme of the next section, namely that barred and oval galaxies
evolve similarly.

Many of the galaxies discussed in the above papers are barred. Those that
are classified as transition objects (SAB) or as unbarred (SA), have
created some uncertainty about how much the star formation depends on
bars. However, many SAB and some SA objects are prototypical oval
galaxies such as NGC 2903, NGC 3504, NGC 4736
(Figures 2 and 8),
NGC 5248, and NGC 6951 (see
Sandage 1961).
We show in Section 3.3 that barred and
oval galaxies are essentially
equivalent as regards gas inflow, star formation, and pseudobulge
building. Section 3.4 suggests that
similar evolution happens in unbarred spirals that do not have an ILR.

We argue in later
sections, as did some of the above authors, that the nuclear star
formation is building pseudobulges. Although the star formation is
frequently in a ring, it is not likely to form a ring of stars. If the
star-forming ring is associated with ILR, then its radius should change
as the central concentration of the galaxy evolves. We expect that the
ring of star formation burns its way through the pseudobulge as it
grows. Also, the spiral dust lanes interior to the star-formation rings
(Figure 8) suggest that gas continues to sink
inside ILR
(Elmegreen et
al. 1998).
Finally, we choose to illustrate star-forming rings, because they most
clearly establish the connection between star formation and bar-driven
secular evolution. However, in many galaxies, the star formation is
spread throughout the central region. An example is NGC 1365
(Figure 7;
Knapen et al. 1995a,
b;
Sakamoto et al. 1995;
Lindblad 1999).

In summary, a comprehensive picture of the secular evolution of barred
galaxies has emerged as simulations of gas response to bars have
succeeded with increasing sophistication in matching observations of
galaxies. Bars rearrange disk gas to make outer rings, inner rings, and
central mass concentrations. SB(s) structure is favored if the bar is
weak or rotating rapidly; SB(r) structure is favored if the bar is
strong or rotating slowly. Because bars grow stronger and slow down as
a result of angular momentum transport to the disk, we conclude that
SB(r) galaxies are more mature than SB(s) galaxies. Consistent with
this, dust lanes diagnostic of gas inflow are seen in SB(s) galaxies
but only rarely in SB(r) galaxies. By the time an inner ring is well
developed, the gas inside it has been depleted. Embedded in this larger
picture is the most robust conclusion of both the modeling and the
observations - that a substantial fraction of the disk gas falls down to
small galactocentric radii in not more than a few billion years. Star
formation is the expected result, and star formation plausibly
associated with bars (concentrated near resonance rings) is seen. These
results provide part of the motivation for our conclusion that secular
evolution builds pseudobulges.